[meteorite-list] meteoroid temperature- Assumptions (P. II)

[MexicoDoug at aol.com]

Part II

Assumptions & Discussion:
T =  [(absorptivity/emissivity)*(Energy  flux/sigma)*(a/A)]^(1/4)
where:
Emissivity = energy ratio emitted at a  temperature = compositional property.
Absorptivity = energy fraction absorbed  at a temperature = compositional 
property.

Temperature is proportional to  absorptivity but proportional to the inverse 
of emissivity, i.e.  T^(4)=k*(absorptivity/emissivity).

The useful form of this law is called  the Stephan-Boltzmann Law:  Energy = 
sigma*T^4 (S-B law constant, sigma =  5.67*10^-8*Wm^-2*K^-4)
That the integrated energy radiated from a black booty  is proportional to 
the fourth power of the temperature.  This "law" is  useful to convert the 
energy hitting an object into the temperature and is  really the scientific key to 
address your question  approximately.

Kirchoff's (other) Law:
For a body in radiative  equilibrium energy absorption = energy emission.  So 
we consider the very  plausible scenario that the meteoroid's position in 
orbit doesn't alter  radically (it doesn't travel near light speed!)
Solar energy is mainly  provided for absorption in the UV-Visible range.
Energy is emitted in the IR  range (vibrational energy, the meteoroid doesn't 
emit much light  energy:-).
Meteoroide is spherical in shape (OK not generality, so could vary  maybe 50% 
either way for example when a planar shaped meteoroid had verrry low  
rotational energy w/r to the Sun)

ABSORPTIVITY = CC = 0.8, OC = 0.65,  Fe-Ni = 0.80, "ideal" = 1
EMISSIVITY = CC = 0.88, OC = 0.85, weathered Fe-Ni  = 0.28, "ideal" = 1

Assumed constant emissivities, but actually they  vary, for example, 
decreasing somewhat (and then only by a square root) as the  AU's increase for Iron, 
and a lot for Nickel, though I expect the "weathered"  surface might somewhat 
mitigate this.

The temperature of a meteoroid in  space will of course depend on the 
latitude, depth, it's cross sectional  exposure vs. overall mass distribution and 
distance to the Sun, just like any  other non-radioactive cooled body whether in 
orbit or passing through.
 
Proximamente: More Assumptions & Discussion